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Graphs of the Sine and Cosine Functions definitions

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  • Unit Circle
    A circle with radius 1 used to relate trigonometric functions to coordinates, forming the basis for graphing sine and cosine.
  • Wave Pattern
    A repeating curve seen in sine and cosine graphs, resulting from periodic values traced from the unit circle.
  • Crest
    A high point on a sine or cosine graph, representing the maximum value reached during a cycle.
  • Trough
    A low point on a sine or cosine graph, representing the minimum value reached during a cycle.
  • Midline
    A horizontal line through the center of a wave, used to measure amplitude and identify vertical shifts.
  • Amplitude
    The distance from the midline to a peak or valley, indicating the height of the wave in sine or cosine graphs.
  • Vertical Shift
    A transformation that moves the entire graph of a function up or down by adding a constant.
  • Reflection
    A transformation that flips the graph over the x-axis, caused by a negative amplitude.
  • Period
    The length along the x-axis for one complete cycle of a wave, calculated using 2π divided by a coefficient.
  • Cycle
    A full sequence of repeating values in a wave, from one crest to the next or one trough to the next.
  • Peak
    A point of maximum value on a wave, synonymous with crest, marking the highest output.
  • Valley
    A point of minimum value on a wave, synonymous with trough, marking the lowest output.
  • Horizontal Stretch
    A transformation that widens the graph, increasing the period when the coefficient inside the function is less than one.
  • Horizontal Shrink
    A transformation that compresses the graph, decreasing the period when the coefficient inside the function is greater than one.
  • Coefficient
    A number placed in front of x inside the function, affecting the period and horizontal transformations of the graph.